DLMF:14.3.E5 (Q4694): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2acdec

Revision as of 01:13, 2 January 2020

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DLMF:14.3.E5
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    𝖯 ν m ( x ) = ( - 1 ) m Γ ( ν + m + 1 ) Γ ( ν - m + 1 ) ( 1 - x 1 + x ) m / 2 𝐅 ( ν + 1 , - ν ; m + 1 ; 1 2 - 1 2 x ) . Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript 1 𝑚 Euler-Gamma 𝜈 𝑚 1 Euler-Gamma 𝜈 𝑚 1 superscript 1 𝑥 1 𝑥 𝑚 2 scaled-hypergeometric-bold-F 𝜈 1 𝜈 𝑚 1 1 2 1 2 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{m}_{\nu}\left(x\right)=(-1)^{m}\frac{% \Gamma\left(\nu+m+1\right)}{\Gamma\left(\nu-m+1\right)}\left(\frac{1-x}{1+x}% \right)^{m/2}\mathbf{F}\left(\nu+1,-\nu;m+1;\tfrac{1}{2}-\tfrac{1}{2}x\right).}}
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    DLMF:14.3.E5
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2acdec
    0 references